Method and apparatus for magnetically controlling motion direction of a mechanically pushed catheter

ABSTRACT

The movement of a catheter through a medium, which may be living tissue such as a human brain, is controlled by mechanically pushing a flexible catheter having a magnetic tip through the medium and applying a magnetic field having a magnitude and a direction that guides the mechanically-pushed catheter tip stepwise along a desired path. The magnetic field is controlled in a Magnetic Stereotaxis System by a processor using an adaptation of a PID (proportional, integral, and derivative) feedback method. The magnetic fields are applied by superconducting coils, and the currents applied through the coils are selected to minimize a current metric.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.09/357,203 filed on Jul. 20, 1999, now U.S. Pat. No. 6,475,223, whichwas a divisional of U.S. patent application Ser. No. 08/920,446 filed onAug. 29, 1997, now U.S. Pat. No. 6,015,414. The disclosures of the aboveapplications are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to devices and methods for moving an implant in abody, and more particularly to such devices and methods that applypushing forces with a flexible attachment and that magnetically steerthe implant in the body with high accuracy.

2. Description of Related Art

There is a large body of conventional (nonmagnetic) stereotactic priorart, in which a frame (e.g., a so-called “BRW Frame”) is attached to theskull to provide a navigation framework. Such a frame has arcs todetermine an angle of an “insertion guide” which is usually a straighttube through which some medical therapeutic agent is passed, such as abiopsy tool. These methods have been confined to straightline approachesto a target.

There is also a smaller body of prior art in which a handheld permanentmagnet or an electromagnet is used to move a metallic implant.

Previous implants for delivering medication or therapy to body tissues,and particularly brain tissue, have generally relied upon the navigationof tethered implants within vessels, or navigation of tethered oruntethered implants moved intraparenchymally (in general brain tissue)by magnetic force.

Navigation of untethered implants, in the past, has generally comprisedfinding ways to apply magnetic force optimally, including both magnitudeand direction, for a given step of “free” motion. However, difficulty infinding a set of currents to accomplish a move step is encounteredbecause of the complexity of calculating the magnetic forces resultingfrom multiple coils.

It is well-known that two like coils on a common axis, having likecurrents, provide a highly uniform magnetic field on their axis at themidpoint between them. In addition, it is known that the field isapproximately uniform for an appreciable region around the midpoint, andrelatively strong, as compared with any other two-coil arrangementhaving the same coil currents. This arrangement of coils and currentsmeets the need for an accurate, strong guiding torque applied to amagnetic implant near the midpoint between the coils. Because the fieldis quite uniform near the midpoint, undesired magnetic forces on theimplant are negligible. However, this arrangement is less suitable for amoving implant when the implant is some distance from the midpointbetween the coils or not on the axis, or when the implant axis is, notalong the coil axis. In these important cases, this simple coilarrangement cannot provide accurate directional guidance. Furthermore,simple vector combinations of three such coil pair arrangements cannotprovide accurate guidance in an arbitrary direction, except at one spotat the center of the arrangement.

The Magnetic Stereotaxis System (MSS) originated from the hopes that aless-invasive methodology could be developed which would allowneurosurgeons to operate in previously inaccessible regions of thebrain. By introducing a small permanent magnetic implant into the brainthrough a small “burr hole” drilled through the skull prior to theoperation, large superconducting coils could be used in conjunction witha pushing mechanism to magnetically guide the implant and overlayingcatheter through the brain's parenchyma, all the while avoiding theimportant structures of the brain. The operational methodology of theMSS was, and continues to be, expected to be less destructive to thetissues of the brain than the shunts, straight tubes, and other devicesassociated with conventional techniques in neurosurgery.

The first MSS was conceptually developed in 1984 as the Video TumorFighter (VTF), and is shown in U.S. Pat. No. 4,869,247 issued Sep. 26,1989. This system specifically focused on the eradication of deep-seatedbrain tumors via hyperthermia-based treatment. It was envisioned thatthe magnetic coils of the VTF would guide a small (˜3 mm diameter)magnetic thermosphere through the brain into a tumor. Rastering theimplant throughout the volume of the growth, the tumor cells could bedestroyed by inductively heating the implant with radio-frequencyradiation.

Further studies revealed that the reality of a magnetomotive basedsystem used to direct a small implant promised numerous applicationsother than the hyperthermia-based treatment of brain tumors byinduction. These included: biopsy, pallidotomy, delivery of precisionradiation therapy, magnetically placed implants that deliverchemotherapy to otherwise inaccessible tumor locations, and (byattaching a semi-permeable catheter to the implant) the delivery ofchemicals to specific sites in the brain without the need forpenetrating the blood-brain barrier which has complicated contemporarysystemic chemical delivery. This means of chemical delivery seemedparticularly hopeful in the treatment of Parkinson's disease, where thecatheter could be used to deliver dopamine to the affected regions ofthe brain with minimal indiscriminate distribution of theneurotransmitter to the surrounding tissue, thereby lessening attendantside effects. It was in the light of these possible broadenedapplications of the VTF that the system became known as the MSS.

Referring now to FIG. 1A and FIG. 1B, the most recent MSS apparatus 10included six superconducting coils (not visible in FIG. 1A and FIG. 1B)located in a rectangular box or helmet 12. With the z-axis defined inthe direction of the axial component of the head, the x- and y-coil axesare rotated 45° from the sagittal plane 14 of the head, which would bepositioned in opening 16. The x- and y-coil axes are symmetricallylocated such that the horizontal extensions 22 of the MSS apparatus 10away from the patient's body is minimized. Because the lower edge of thetreatable part of the brain is typically located 10 cm above theshoulder line for an average adult, the z-coils (located on thebody-axis of the supine patient) were compressed to allow for a maximumextension of the head into helmet 12.

The vision component of the MSS consists of a superposition ofpre-operative MRI images referenced by biplanar fluoroscopy cameras 20linked to a real-time host system (not shown in FIG. 1A and FIG. 1B).Both cameras 20 are calibrated to the MSS six-coil helmet design. X-raygenerators for cameras 20 are located inside magnetic shields 22. Usingx-ray visible fiducial markers located on the skull of the consciouspatient, the coordination of the implant's position inside the cranialvolume to the helmet's reference system (and hence the correspondingpreoperative MRI scan) is done through a series of coordinatetransformations executed by a host system and displayed for the surgeonon a workstation.

The central problem to the inductively-based guidance of a magneticimplant pertains to the inverse problem of electromagnetism asinfluenced by Earnshaw's theorem. The conventional problem ofelectromagnetism centers on the evaluation of the gradient and magneticfield given established magnetomotive sources. For the MSS, however, thesituation is reversed in that the magnetic field and its gradient arespecified at a point in space while the strengths of the six actuatorsare to be determined. Control of the motion and position of anuntethered implant would be difficult in the MSS, given the fundamentalinstability of a non-diamagnetic moment in a static or quasi-staticmagnetic field as related to Earnshaw's theorem for static/quasi-staticmagnetic fields, if it were not for the resistive nature of theparenchyma. In early tests, small cylindrical (up to 5 mm in length and5 mm in diameter) permanently magnetized NdBFe objects were used. Therelatively strong moment of these objects (0.016 A−m² to more than 0.04A−m²) facilitated the creation of the necessary aligning torque withoutthe requirement of a strong magnetizing field, resulting in lowercurrent values.

The permanent magnetization of the implant requires a predeterminedmagnetic field in order to ensure that the implant is oriented in thedesired direction. While it is possible to generate a magnetic force todisplace the implant, it was found that the requirement of specificforce and field alignment could result in unobtainable currents (as highas thousands of amperes). It was also found that even for viablesolutions, the equilibrium state was sometimes unstable to such anextent that the implant tended to be difficult to control.

SUMMARY OF THE INVENTION

The invention is an apparatus and method for moving an implant in thebody by applying pushing forces with a flexible attachment andmagnetically steering the implant in the body with high accuracy andcontrollability. Because the intended moving force is appliednon-magnetically, it is possible and desirable to apply currents in themagnetic steering apparatus in such combinations as to maximize themagnetic field at a body location inside the coil array to therebyprovide optimal directional guidance torque on an implant whileminimizing undesired translational force on the implant.

According to one aspect of the invention, there is provided a method forcontrolling movement of a catheter through a medium, in which a flexiblecatheter having a magnetic tip is pushed through a medium, and amagnetic field having a magnitude and orientation effective to guide themechanically-pushed catheter tip in a predetermined direction isapplied.

According to another aspect of the invention, a method for providingstepwise movement of a catheter having a magnetic tip is provided, inwhich the method includes the steps of selecting a desired path of thecatheter through living tissue, inserting the catheter tip into theliving tissue, determining actual positions of the magnetic tip andcorrection vectors (the correction vectors representing differencesbetween locations on the desired path and the actual positions of themagnetic tip), storing values of correction vectors in a memory, andapplying a magnetic field adjusted to achieve movement of the magnetictip at least approximately along the desired path, the adjustmentdepending upon at least one stored set of values of correction vectors.

Also provided is a device for guiding a catheter having a magnetic tipthrough a medium, the device comprising a helmet having a cavityconfigured to encompass a medium through which a catheter is to beguided, a magnetic field generator generating a magnetic field withinthe cavity, a position sensor sensing a location of a magnetic tip of acatheter in the cavity and generating a signal indicative of the sensedlocation, an advancement mechanism pushing the magnetic tip of thecatheter through the medium, and a processor responsive to the signalfrom the position sensor and having an operator control input, theprocessor being configured to control the magnetic field generated bythe magnetic field generator in response to commands input via theoperator control input and the signal received from the position sensor.

The above embodiments may also incorporate significant additionalimprovements, including, for example, the minimization of a currentmetric, so that the proper magnetic field to guide the magnetic tipthrough the medium is generated with a near-minimum amount of current.

The methods and apparatuses of this invention provide the ability tomore accurately direct a seed or catheter in the brain or other parts ofthe body, including the path to that position. Highly accuratedirectional guidance of implants is possible over arbitrary nonlinearpaths, and the implant can be guided freely through tissues such asbrain tissue, without being limited to the interior of vessels.

Additional advantages of the present invention over prior art systemsare that:

(1) Solutions applicable to guiding an implant on a predetermined pathare simpler, and thus, are found more rapidly and with less likelihoodof error for a given step of motion.

(2) Solutions are much more stable than with prior art systems, and arefree of runaway conditions.

(3) Currents applied by the new method are generally considerablysmaller than with previous methods; therefore, the current changesbetween steps are smaller, allowing changes to be made much more rapidlyand accurately between steps, and with less possibility of quenchingsuperconducting magnets.

(4) Guidance force occurs without skid, which is a condition in whichthe magnetic field that orients the implant and the magnetic force arein different directions so that the axis of the implant skids along thepath.

(5) Currents are applied in a simple temporal fashion, moving directlyfrom one set to another set between two steps of motion. The actualforce impulse causing each step of motion is from the duration anddistance of the externally applied non-magnetic force during that step.(Prior art systems ramped currents from conditions for subthresholdforce to that of a moving force and then back down below threshold atthe appropriate time, which is a complex dynamic sequence subject tosubstantial error in step length due to the tribological nature of theimplant and tissue.

(6) Navigation can now occur continuously rather than in steps.

It is thus an object of the invention to provide a method forcontrolling the motion of a catheter in any predetermined direction.

It is a further object of the invention to control the motion of acatheter by applying a torque to the catheter to guide its directionwith a reliable, predictable strength.

It is yet another object of the invention to control the motion of acatheter rapidly, accurately, and reliably, even when the magneticsystem used in conjunction with the catheter includes superconductingcoils that are vulnerable to misoperation from too rapid currentchanges.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are views along the Z-axis and into the cavity of oneembodiment of a Magnetic Stereotaxis System (MSS), respectively;

FIG. 2 is a simplified representation showing the orientation ofsuperconducting coils within the helmet of an MSS;

FIG. 3A is drawing of a portion of a catheter having a metal tip, andFIG. 3B is a drawing of a magnetic element and push wire within thecatheter of FIG. 3A;

FIG. 4 is a diagram showing various points and vectors along a desiredpath of a catheter tip, in which the points and vectors shown aresignificant for the calculation of the magnetic field needed to guidethe tip in accordance with the invention;

FIG. 5 is a block diagram of a portion of a Magnetic Stereotaxis Systemin accordance with the invention;

FIG. 6 is a block diagram of another portion of the Magnetic StereotaxisSystem of FIG. 5; and

FIG. 7 is a block diagram of a configuration of a processor suitable foruse in the MSS of FIGS. 5 and 6.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention is described herein in the context of guiding an implantinside a brain because tests have been performed for this case. However,those skilled in the art will recognize that the invention is applicableto other parts of the body and to other media through which a magnetictip at the end of a flexible catheter can be pushed.

In the present example, a system of six coils is provided. Referring toFIG. 2, which is a simplified representation of the coil geometry, thecoils X+, X−, Y+, Y−, Z+, and Z− are operated in unbalanced pairs (X+,X−), (Y+, Y−), (Z+, Z−) acting approximately as three vectors X, Y, andZ having mutually perpendicular directions, but different magnitudes.The operation is achieved in a manner that is effective at positions offthe axis of any or all of the three pairs of coils (X+, X−), (Y+, Y−),(Z+, Z−) constituting the helmet (or other coil support arrangement).

The method for controlling the path in the Magnetic Stereotaxis System(MSS) includes calculations involving vectors that represent desiredpath steps and corrective feedback vectors in an inventive adaptation ofa well-known PID (proportional, integral, and derivative) feedbackmethod. However, the operations here are on the motion of a magneticimplant. Referring to FIGS. 3A and 3B, the magnetic implant 30 acts as aleading element (the “directing train engine,” which is called amagnetic delivery vehicle or MDV) and which is only part of the overallmoving unit which also includes a pushing stylette 32 driven by a motor(not shown) which supplies a force F. Stylette 32 and implant 30 aresurrounded by flexible catheter 34, which has a metal tip 36 at the endwithin which MDV 30 is located. The method and apparatus of thisinvention controls the curving elements of the catheter.

For the purposes of this discussion of the invention, the term “lag” isapplied to the angle by which the catheter would fall outside a curvethat would be followed by a completely limp catheter. During magneticnavigation, the MSS system monitors the position of the catheter tip(the MDV) versus a desired position in accordance with a planned path.Referring to FIG. 4, corrections are made in accordance with afeedback/lag model that is given by the equation

$\begin{matrix}{{V_{step} = {V_{path} + V_{lag} + {g\frac{V_{correction}}{V_{correction}}}}},} & (1)\end{matrix}$

in which:

V_(lag) is a lag-correction vector pointing to an inside of a localcurvature of the planned path indicated by R at point p₂; and

g is a gain factor; and

V_(path) is constructed by finding a point p₁ on the planned pathclosest to the present actual position, and then finding a point p₂further along the planned path which matches the length of the intendedstep. Then V_(path)=p₂−p₁;

V_(correction) is a vector from the actual position to the point on thepath closest to the present actual position (i.e., a direction oppositean “error vector”); and

V_(step) is the resultant direction that the next step should take,corrected for lag.

The direction of V_(step) is constrained to vary from move to move in amanner so that sudden changes in V_(step) result in a path having aspecified minimum radius of curvature or a less curved trajectory. Thevalue of g is computed and adjusted for each step by means of a PIDmodel in whichg=∥k _(p) V _(c(n)) +k _(i)(V _(c(n)) +V _(c(n−1)) +V _(c(n−2)))+k_(d)(V _(c(n)) −V _(c(n−1)))∥, where:

k_(p), k_(i), and k_(d) are predetermined constants that may be found byexperiment; and

V_(c(n)), c_(c(n−1)), and V_(c(n−2)) are the correction vectors at thenth step (present step), the previous (n−1)th step, and the (n−2)thsteps, respectively.

It is noted that what here is called a “correction vector” is thenegative of what is often called an “error vector.” The term “correctionvector” rather than “error vector” has been used throughout thisdescription for convenience. However, this usage is not intended to belimiting in any way, because those skilled in the art will recognize theequivalence of “correction vectors” and “error vectors” and thenotational changes that would be required by the substitution of one forthe other.

When the correction vectors at the nth, (n−1)th, and (n−2)th steps areused in the correction vector V_(step), they become an approximation toan integral mode of control. That is, a correction is made proportionalto the integral of the recent path errors. Similarly, an approximatederivative or rate correction is made when the difference(V_(c(n))−V_(c(n−1))) of the present and most recent correction vectorsis used as a term in V_(step).

In one exemplary MSS implementation, vector V_(lag) was determinedexperimentally by attempting to drive a magnetic catheter tip (such astip 36 in FIG. 3A) in a circle of predetermined radius, but settingV_(lag)=0. The catheter was driven by a motor providing a constantadvancement rate through a phantom gel, which provided some friction.Where there is such friction, an equilibrium arises because the forcefrom the gel counteracts the force from the magnetic field and tends tobalance it at some point before alignment of movement with the magneticfield is achieved. In this case, the counterbalancing force of thegel-simulated the counterbalancing force of actual brain tissue, and asexpected, the magnetic tip spiraled outward from the circle in adirection a few degrees out of alignment with the magnetic field.V_(lag) was then experimentally set to be the vector correction thatwould have been necessary to provide to counteract the deviation fromthe circular path.

By increasing the magnitude of the field, the magnitude of V_(lag) canbe reduced. However, it is also desirable to at least approximatelyminimize the coil currents required to generate the magnetic field.Experiments have shown that, for the particular set of coils in one MSSapparatus, with a motor pushing a catheter along the magnetic field at arate of about 0.5 mm/s, there was little decrease in V_(lag) for fieldsgreater than about 0.3 Tesla. Therefore, in the experiment to determineV_(lag), as well as in other tests, the magnetic field was constrainedto have a magnitude no greater than 0.3 Tesla. This value has beenfound, by experiment, to be sufficient to orient the direction ofmovement of a magnetic tip of a catheter being pushed by a motor at 0.5mm/s through a phantom gel. It will be understood that the necessarymagnetic field magnitude may vary if different catheters, motors, ormagnetic tips are used, or if a different advancement rate is applied.

Correction according to V_(lag) is a single-parameter means ofanticipating error that would occur due to restoring torques from anattached pushing element. A person skilled in the art would recognizethe close relationship of this action to the concept of “feed-forward”in the field of control theory. It is intended, according to one aspectof the invention, that the inventive apparatuses and techniques may beuseful for applications in which a simple feed-forward correction is notadequate. In such applications, a computer or processor will have arepresentation of a planned or predetermined path stored in its memory.At any location or locations where the planned path deviates from astraight line in front of a then-present location of the seed, a programstored in the computer provides an added correction vector, which may bea function of several different parameters, to provide a bettercorrection than V_(lag) by anticipating future error in the absence ofsuch correction. As one example, if a planned path curves in more thanone plane, a correction vector can contain terms which have correctionvector components in each of the planes. The weighting of thesecomponents preferably varies as the inverses of the individual radii ofcurvature, and are also preferably weighted inversely according to thedistance from the present seed position at which the particularcurvatures occur. These parameters can be readily calculated by aprogram stored in the memory of the computer. It is thus possible, andmay be preferable, to use information related to a future location ofthe seed to guide the seed, and/or a determined rate of change in theobserved correction vectors in addition to information stored in memoryabout its past position and errors.

With respect to the gain parameters k_(p), k_(i), and k_(d), it has beenexperimentally determined that, for the tested MSS apparatus, it issufficient to set k_(p)=0.5, k_(i)=0.5, and k_(d)=0. The parameterk_(d), which effectively adjusts the speed of response of the system,can be set to zero because the system response obtained has beensatisfactory for the relatively slow tip advancement rate of 0.5 mm/s.In addition, setting k_(d)=0 has the advantage of reducing noise in thesystem, because the imaging method used to locate the magnetic tip(biplanar x-ray imaging) has provided an accuracy only within about ±1.0mm. Adjusting the system gain by increasing the magnitude of k_(d) wouldresult in significant noise amplification without a concomitant increasein position sensing accuracy. If more accurate methods of determiningthe location of the seed were used, it would be practical to use anonzero value of k_(d) to provide more rapid system response. This morerapid system response could permit an increase of the tip advancementrate above 0.5 mm/s in appropriate medical procedures, which may shortenthe time necessary to perform such procedures.

Once the vector V_(step) is determined, representing a vectorcorresponding to a motion of the magnetic tip at least approximately inthe direction of the desired path, the coil currents necessary togenerate the required field must be determined. In general, this problemis underdetermined in that many different sets of coil currents could beused to generate the required field, and, without the addition offurther constraints, solutions can be obtained that require impracticalamounts of currents in some or all of the coils. A method of determiningpractical values of coil currents that generate a sufficient magnitudemagnetic field in the correct direction at the location of the magnetictip has been found, and is described herein.

For controlling superconducting or normally conducting coils, theroot-mean-square value of the coil currents (the coil-current metric) isminimized while the strength and direction of the magnetic field remainat the desired values. (The magnetic field is linear with respect to thecoil currents.) This constraint removes three of the six degrees offreedom in selecting the six coil currents, leaving a quadratic equationfor the current metric. This metric is minimized to compute the optimalcoil currents. While minimizing the current metric does not necessarilycorrespond to minimizing the individual current magnitudes, it is auseful and efficient way of ensuring that the current magnitudes arekept at a sufficiently low level for purposes of the invention.

The m equality, linearly constrained quadratic problem is stated as

$\begin{matrix}\left. {{\left. \begin{matrix}{{{Maximize}\mspace{14mu} z} = {{\sum\limits_{i = 1}^{n}{x_{i}c_{i}}} + {\sum\limits_{i,{j = 1}}^{n}{x_{i}P_{ij}x_{j}}}}} \\{{{Subject}\mspace{14mu}{to}\mspace{14mu}{\sum\limits_{j = 1}^{n}{D_{ij}x_{j}}}} = {e_{j}\mspace{14mu}\left( {{i = 1},\ldots\mspace{11mu},m} \right)}}\end{matrix} \right\}\mspace{14mu}{or}}\mspace{11mu}\;\begin{matrix}{{{Maximize}\mspace{25mu} z} = {{x^{T}c} + {x^{T}{Px}}}} \\{{{Subject}\mspace{14mu}{to}\mspace{14mu}{Dx}} = e}\end{matrix}} \right\} & (2)\end{matrix}$where xε

^(n). We assume that the conditions Dx=e comprise a non-degenerate setwith m<n. If m>n, then the system is over specified and no solution mayoccur. In the case that m=n, then one solution exists at the pointx_(o)=D⁻¹e providing |D|≠0. Hence, no optimization is possible ornecessary.

Constructing the Lagrangian, we find thatL=x ^(T) c+x ^(T) Px+λ ^(T)(Dx−e)  (3)where m Lagrange multipliers have been introduced. From the Lagrangian,we obtain the global extremum

$\begin{matrix}{\begin{Bmatrix}x_{o} \\\lambda_{o}\end{Bmatrix} = {\begin{Bmatrix}{2P} & D^{T} \\D & 0\end{Bmatrix}\begin{Bmatrix}{- c} \\e\end{Bmatrix}}} & (4)\end{matrix}$where it is assumed that the matrix inversion is possible.

To particularize this result to the minimization of the current metricfor the MSS, we begin by focusing solely on the static and quasi-staticcases, thus assuming that the source currents are either held constantor ramped relatively slowly in time. Given n magnetomotive sources (or,in this sense, actuators), we wish to operate the sources with minimalcurrents so that a desired magnetic field may be specified for aselected point in space x_(o) where x_(o)ε

. The total magnetic field at any point x, b(x), is the linearsuperposition of the magnetic fields due to each source evaluated at x:

$\begin{matrix}{{b(x)} = {\sum\limits_{i = 1}^{n}{b_{i}(x)}}} & (5)\end{matrix}$Since b_(i)(x) is linear with respect to its corresponding sourcecurrent, I_(i), the above may be written as

$\begin{matrix}{{b\left( {x,I} \right)} = {\sum\limits_{i = 1}^{n}{{{\overset{\_}{B}}_{i}(x)}I_{i}}}} & (6)\end{matrix}$where B _(i)(x) consists of the three current-independent components ofthe magnetic field for each source. If we define the 3×n matrix B(x) asB (x)={ B ₁(x) | B ₂(x)| . . . | B _(n)(x)}  (7)and we write the currents as the n-element column vector I, then Eq. (6)and Eq. (7) can be combined to form the matrix relationshipb(x,I)= B (x)I  (8)Note that n>3 is assumed in order for an optimization to be made for adesired magnetic field b (which consists of three components). If n<3(i.e., two actuators or less), the system is over constrained and nosolution exists unless there is a degeneracy in Eq. (8). If n=3, thenthe solution to the currents, I_(o), is given byI _(o) = B ⁻¹(x _(o))b.

We now focus our attention on the current metric defined as

$\begin{matrix}{{z(I)} = {{\sum\limits_{i = 1}^{n}I_{i}^{2}} = {I^{T}I}}} & (9)\end{matrix}$While the metric does not specifically limit the individual currents, itdoes serve as a means of penalizing those solutions that are associatedwith strong currents. The problem of finding an optimal set of currents(for n>3 sources) may now be stated in a form for which there are m=3equality constraints:

$\begin{matrix}\left. \begin{matrix}{{{Maximize}\mspace{14mu}{z(I)}} = {{- I^{T}}I}} \\{{{Subject}\mspace{11mu}{to}\mspace{14mu}{\overset{\_}{B}\left( x_{o} \right)}I} = b}\end{matrix} \right\} & (10)\end{matrix}$It is noted that we could just as easily minimize the current metricabove without loss of generality; however, writing the problem in theform of Eq. (10) is convenient for our present purposes. Since themetric of Eq. (10) is a concave function, the solution for the currentsis:

$\begin{matrix}{\begin{Bmatrix}I_{o} \\\lambda_{o}\end{Bmatrix} = {\begin{Bmatrix}{{- 2}I_{D}} & {\overset{\_}{B}\left( x_{o} \right)}^{T} \\{\overset{\_}{B}\left( x_{o} \right)} & 0\end{Bmatrix}^{- 1}\begin{Bmatrix}0 \\b\end{Bmatrix}}} & (11)\end{matrix}$where I_(D) is the identity matrix. Inspection of Eq. (10) reveals thatonly one extremum (and hence, the global maximum) of the negativecurrent metric can occur. Eq. (11) thus provides the solution for thecoil currents I_(o) in the MSS given a specified magnetic field.

While the current metric is sufficient in restricting the currents tosmall values in most cases, it does not minimize them. It is possiblethat a larger metric results when smaller currents are distributed overseveral sources. For example, say the desired field for a four sourcesystem corresponds to the optimal set of currents I_(o) ^(T)={10 80 1080}(A) for which z(I_(o))=13000 A². If the individual currents must beless than 75 A, another (possibly more useful solution in some cases)would correspond to I_(o) ^(T)={60 70 60 70}(A), for whichz(I_(o))=17000 A², providing the currents generate the same magneticfield. Including the k linear current limits DI≧e into Eq. (10), ourgeneral n-source, linearly constrained problem is stated as

$\begin{matrix}\left. \begin{matrix}{{{Maximize}\mspace{14mu} z} = {{- I^{T}}I}} \\{{{Subject}\mspace{11mu}{to}\mspace{14mu}{\overset{\_}{B}\left( x_{o} \right)}I} = b} \\{\mspace{115mu}{{DI} \geq e}}\end{matrix} \right\} & (12)\end{matrix}$Since it is more commonly found that the n actuators possess upper andlower limits according to |I_(i)|≦I_(max). (i=1, . . . , n), theconstraints form a closed and bounded set providing the specification ofB still holds for the range of allowed currents. The problem becomes

$\begin{matrix}\left. \begin{matrix}{{{Maximize}\mspace{14mu}{z(I)}} = {{- I^{T}}I}} \\{{{Subject}\mspace{11mu}{to}\mspace{14mu}{\overset{\_}{B}\left( x_{o} \right)}I} = b} \\{{\begin{Bmatrix}I_{D} \\{- I_{D}}\end{Bmatrix}I} \geq {- \begin{Bmatrix}I_{\max} \\I_{\max}\end{Bmatrix}}}\end{matrix} \right\} & (13)\end{matrix}$where k=2n inequality constraints with I_(max,i)=I_(max) for i=1, . . ., n have been introduced. The conditions that must be satisfied in orderfor maximum to exist are given by

$\begin{matrix}\left. \;\begin{matrix}{{{{- 2}I_{o}} + {\mu_{o}^{T}\begin{Bmatrix}{- I_{D}} \\I_{D}\end{Bmatrix}} + {\lambda_{o}^{T}{\overset{\_}{B}\left( x_{o} \right)}}} = 0} \\{{\mu_{o}^{T}\left( {{\begin{Bmatrix}{- I_{D}} \\I_{D}\end{Bmatrix}I_{o}} + \begin{Bmatrix}I_{\max} \\I_{\max}\end{Bmatrix}} \right)} = 0} \\{{{\overset{\_}{B}\left( x_{o} \right)}I_{o}} = b} \\{{- I_{\max}} \leq I_{o} \leq I_{\max}} \\{\mu_{o} \geq 0}\end{matrix} \right\} & (14)\end{matrix}$The possible 2^(2n)=4^(n) solutions of the above set of equations followfrom Eq. 29 of Appendix B where individual constraints are activatedamong the 2n inequality conditions. As was previously discussed, whenthe activated constraints combined with the equality constraintsoutnumber the degrees of freedom, the system of equations become overspecified and no solution need be calculated. For those cases in whichthe system of equations is exactly specified, the solution must bechecked against the inequality constraints to deem it viable. Thereremain

$4^{n} - {\sum\limits_{i = {n - 3}}^{2n}\frac{2{n!}}{{\left( {{2n} - i} \right)!}{i!}}}$of the 4^(n) cases which can be solved (assuming a solution exists).Those solutions that satisfy the constraints are saved and the set thatresults in the maximum value of z(I_(o))=−I_(o) ^(T)I_(o) [or minimum ofz(I_(o))=I_(o) ^(T)I_(o)] is reported as the optimal solution.

It is sometimes useful to restrict the magnetically generated force on asmall permanent moment. For example, quasi-static systems such asmagnetic suspensions and the MSS can profit from an inclusion of forceconstraints if higher currents are acceptable. The force at x_(o),f(x_(o)), generated on a small permanent magnetic moment, m, due to amagnetic field, b, is given byf(x _(o))=∇(m ^(T) b(x))|_(x=x) _(o)   (15)An easier notation for the present purposes involves writing the threecomponent of the force as

$\begin{matrix}{{f_{i}\left( x_{o} \right)} = {m^{T}\frac{\partial b}{\partial x_{i}}\left( x_{o} \right)\left( {{i = 1},2,3} \right)}} & (16)\end{matrix}$For those problems in which the moment is allowed to align with themagnetic field

$\left\lbrack {{i.e.},{m = {\frac{m}{b}{b\left( x_{o} \right)}}}} \right\rbrack,$Eq. (16) is transformed into

$\begin{matrix}{{f_{i}\left( x_{o} \right)} = {{\frac{m}{{b\left( x_{o} \right)}}{b\left( x_{o} \right)}^{T}\left( \frac{\partial{b(x)}}{\partial x_{i}} \right)}❘_{x = x_{o}}\mspace{14mu}\left( {{i = 1},2,3} \right)}} & (17)\end{matrix}$where the strength of the moment ∥m∥ is known. Combining the results ofEq. (17) with Eq. (8), a somewhat complicated problem arises for thosecases in which the orientation of the magnetic field at x_(o) isunrestricted. This can be seen in the nonlinear form of

$\begin{matrix}{{f_{i}\left( {x_{o},I} \right)} = {{m}I^{T}{\overset{\_}{B}\left( x_{o} \right)}^{T}\left( {\frac{\partial\overset{\_}{B}}{\partial x_{i}}\left( x_{o} \right)} \right)\frac{I}{\sqrt{I^{T}{\overset{\_}{B}\left( x_{o} \right)}^{T}{\overset{\_}{B}\left( x_{o} \right)}I}}\mspace{14mu}\left( {{i = 1},2,3} \right)}} & (18)\end{matrix}$For the present purposes, only those cases that rely on a specifiedmagnetic field are considered.

Using the current dependence of the magnetic sources and a predeterminedmagnetic field b where b= B(x_(o))I, Eq. (17) can be written in twoforms. The linear and quadratic forms are given by, respectively,

$\begin{matrix}{{{f_{i}\left( {x_{o},I} \right)} = {\frac{m}{b}{b^{T}\left( {\frac{\partial\overset{\_}{B}}{\partial x_{i}}\left( x_{o} \right)} \right)}I\mspace{14mu}\left( {{i = 1},2,3} \right)}}{and}} & (19) \\{{f_{i}\left( {x_{o},I} \right)} = {\frac{m}{b}I^{T}{\overset{\_}{B}\left( x_{o} \right)}^{T}\left( {\frac{\partial\overset{\_}{B}}{\partial x_{i}}\left( x_{o} \right)} \right)I\mspace{14mu}\left( {{i = 1},2,3} \right)}} & (20)\end{matrix}$While the form of Eq. (19) may appear more useful, at least sevenactuators must be present in order to overcome the six constraints dueto the specification of the magnetic field and force. If it is importantthat both the force and field be specified and if there are a sufficientnumber of actuators, then the work follows from Eq. (10)-Eq. (14) withthe three additional force constraints being included into the fieldconstraints. If there are exactly six actuators, then there exists aunique solution to the problem at

$\begin{matrix}{I_{o} = {\begin{Bmatrix}\left( {{\frac{m}{b}{\bigtriangledown\left( {b^{T}{\overset{\_}{B}(x)}} \right)}}} \right)_{x = x_{o}} \\\overset{\_}{B}\end{Bmatrix}^{- 1}\begin{Bmatrix}f \\b\end{Bmatrix}}} & (21)\end{matrix}$providing the operating matrix is invertible and the currents areunbounded.

More often than not, the experimenter is more concerned with eitherminimizing a component of the force or the strength of the force withrespect to a limited range of currents and a desired magnetic fieldrather than specifying a specific value of the force. If examining acomponent of the force, Eq. (20) is generalized so that the force alongthe unit vector u (∥u∥=1) is minimized. The force component of interestbecomes u^(T)f(x_(o),I) and the problem is written as

$\begin{matrix}\left. \begin{matrix}\begin{matrix}{{{Maximize}\mspace{14mu}{z(I)}} = {{{- u^{T}}{f\left( {x_{o},I} \right)}} = {- \frac{m}{b}}}} \\{\left( {{\sum\limits_{{i = 1},2,3}}u_{i}I^{T}{\overset{\_}{B}\left( x_{o} \right)}^{T}\left( {\frac{\partial\overset{\_}{B}}{\partial x_{i}}\left( x_{o} \right)} \right)I} \right)}\end{matrix} \\{{{Subject}\mspace{11mu}{to}\mspace{14mu}{\overset{\_}{B}\left( x_{o} \right)}I} = b} \\{\mspace{115mu}{{\begin{Bmatrix}I_{D} \\{- I_{D}}\end{Bmatrix}I} \geq {- \begin{Bmatrix}I_{\max} \\I_{\max}\end{Bmatrix}}}}\end{matrix} \right\} & (22)\end{matrix}$Likewise, if the force strength is to be minimized, a quadratic form isobtained for the objective function by squaring the force components ofEq. (19):

$\begin{matrix}\left. \begin{matrix}\begin{matrix}{{{Maximize}\mspace{14mu}{z(I)}} = {{{- {f\left( {x_{o},I} \right)}^{T}}{f\left( {x_{o},I} \right)}} = {- \left( \frac{m}{b} \right)^{2}}}} \\{\left( {{\sum\limits_{{i = 1},2,3}}{I^{T}\left( {\frac{\partial{\overset{\_}{B}}^{T}}{\partial x_{i}}\left( x_{o} \right)} \right)}{{bb}^{T}\left( {\frac{\partial\overset{\_}{B}}{\partial x_{i}}\left( x_{o} \right)} \right)}I} \right)}\end{matrix} \\{{{Subject}\mspace{11mu}{to}\mspace{14mu}{\overset{\_}{B}\left( x_{o} \right)}I} = b} \\{\mspace{115mu}{{\begin{Bmatrix}I_{D} \\{- I_{D}}\end{Bmatrix}I} \geq {- \begin{Bmatrix}I_{\max} \\I_{\max}\end{Bmatrix}}}}\end{matrix} \right\} & (23)\end{matrix}$If it is desired that the force be maximized rather than minimized, thenthe negative sign to the objective function is left off in Eq. (22) andEq. (23). The conditions that establish the existence of a minimum ormaximum follow from Eq. 27 of Appendix A. Note that only for forceminimizations may the currents be left unbounded.

Portions of the above description of hardware and control methods andapparatuses refer to a six-coil system for use in certain applicationsin the medical field. However, the invention is not limited to systemshaving any particular number of coils, and is suitable for applications(including magnetic surgery applications) for which other coil numbersand arrangements may be preferable. For example, it is possible toremove the front coil of the above system, and to bring side coilscloser together. The resulting five-coil arrangement would allow thepatient to be more accessible to a surgeon, an important considerationfor some surgical procedures. Other arrangements with different numbersof coils may be particularly useful with some other types of operations,for example, those at locations in the body other than the head. (Itshould be noted that it is not required by the invention thatembodiments of multiple coil systems necessarily have coils that areoperated in pairs, opposed or otherwise. Thus, the invention alsoencompasses systems having arbitrary numbers of coils.)

An apparatus that controls coil currents and magnetic tip advancement isillustrated in block diagram form in FIG. 5 and FIG. 6. (It should benoted that not all external connections to console 54 are shown in eachfigure.) FIG. 5 shows a catheter 34 with metal tip 36 having a magneticimplant 30 inside (see also FIG. 3A). This catheter is shown with tip 36already implanted in the brain of a patient 50, at the beginning stagesof a medical procedure. Push wire 32 is operatively coupled to a motorin an advancement mechanism 52 that a surgeon may control by issuingcommands at a console 54. Console 54 includes a real-time computerhaving a display screen 56 and an operator control 58, which may be akeypad or other convenient data entry device. Although the apparatus isdescribed in conjunction with operations on a catheter in the brain ofpatient 50, it should be recognized that the inventive apparatus andtechniques may be applied to other living tissues as well, or in othermedia, living or not, through which it may be desired to push a magnetictip on a flexible push wire or guide wire.

Referring now to FIG. 6, the head of patient 50 (not shown in FIG. 6) isdisposed in opening 16 of coil apparatus 10, as the surgeon operates theinventive apparatus. Console 54 contains a processor such as a digitalcomputer responsive to operator commands input through operator control58 and to cameras 20 for controlling a power supply (not shown) thatsupplies currents to coil terminals 24 to generate the required magneticfields. To fully automate the catheter movement, advancement mechanism52 may also be controlled by the processor. Cameras 20 and X-raygenerators inside magnetic shields 22 provide magnetic tip positioninformation to the processor in console 54. It will be recognized,however, that other suitable means for providing position informationmay be substituted for the cameras 20 and X-ray generators.

To perform a procedure, a surgeon would observe the initial position ofthe magnetic tip 36 with the aid of console 54 and plan a path throughthe tissue of patient 50 (in this case, the brain) to a point at whichtreatment is to be delivered. The surgeon may also choose a step sizeand an advancement rate, although either or both of these may bepreprogrammed. The surgeon then activates the system by issuingappropriate commands through console 54.

In response to these commands, the processor inside console 54 computespositions of metal tip 36 from data received from cameras 20, as well asvectors V_(step) and the coil currents necessary to move metal tip 36along the desired path at the beginning of each step, and applies thecomputed currents to the coils while advancement mechanism 52 advancesmetal tip 36 through the tissue. Correction vectors V_(correction) arestored in memory to provide the necessary history for the PIDcalculations. The advancement continues until the endpoint of the pathis reached. Although the advancement occurs in steps, the positions andcoil currents can typically be calculated rapidly enough to make theadvancement of magnetic tip 36 essentially continuous.

If necessary, the surgeon may intervene by stopping movement of thecatheter or by changing its course before the originally plannedendpoint is reached. When a course change is made, the correctionvectors V_(correction) stored in the memory of the processor duringadvancement on the aborted path are either cleared from memory or simplyignored so that these vectors do not influence the calculationsperformed to direct the magnetic tip along the new path.

FIG. 7 shows a simple block diagram of a manner in which a processor 90may be configured for use in console 54. Processor 90 is provided withoperator control 58 (which may, for example, be a keyboard) foraccepting operator input and a display 56 for displaying information tothe operator. Inputs and outputs 70, 74, 76, 78, and 80 corresponding tothose shown in FIG. 5 and FIG. 6 are provided to obtain data requiredfor sensing position of the catheter tip and for controlling the X-rayfluoroscopes and superconducting coils inside helmet 12. A random accessmemory 94 is provided for storing values of V_(correction), and aprogrammable power supply 92 is provided to supply current to thesuperconducting coils through a plurality of lines 72 in accordance withthe current values computed by processor 90. Although programmable powersupply 92 is shown as a power supply having multiple, independent,programmable outputs, it will be readily appreciated that a plurality ofindividual power supplies may be used as an alternative to the powersupply shown in the figure.

A document describing the structure of a computer program to operate aprocessor in accordance with the invention is attached as Appendix A.Computer programs written in the C++ computer language that determineand control current applied to the coils in accordance with theinvention appear in Appendix B. A more detailed treatment of quadraticoptimizations pertaining to current solutions for magnetic field sourcesappears in Appendix C. A more detailed treatment of the generation of amagnetic field for a circular coil of distributed current appears inAppendix D. A detailed mathematical treatment of the summation of fieldcomponents for single and multiple coils appears in Appendix E, whichcontinues the discussion of the material in Appendix D.

The above-described embodiments are intended to be illustrative only.For example, there are numerous types of magnetic surgery procedures forwhich the coil systems described and the method of calculating andproviding currents to generate fields and forces are important, but forwhich there is no planned or predetermined path and no feedback.Instead, a device in accordance with the general principles of theinvention can provide magnetic guidance of a tip of a surgical devicesuch as a catheter, endoscope, etc. The invention can be readily adaptedso that a surgeon, under guidance from an imaging system, uses themagnetic system to negotiate otherwise difficult turns and movements ofthe surgical device as he or she pushes a device along the interior of avessel. It will also be recognized that many of the inventive methodsand apparatuses may be used in conjunction with any coil in anon-resonant circuit that applies a magnetic force on a suspended orembedded object that is magnetically moveable. Many other modificationsfalling within the spirit of the invention will be apparent to thoseskilled in the art. Therefore, the scope of the invention should bedetermined by reference to the claims below and the full range ofequivalents in accordance with applicable law.

1. A method of navigating a medical device through the body, the methodcomprising the steps of: mechanically pushing the medical device toadvance the distal end of the medical device through the body; while themedical device is being mechanically pushed, applying a magnet fieldfrom a source outside the body to a magnetically responsive elementadjacent the tip of the medical device, the field being of sufficientmagnitude and orientation to change the direction of the tip of themedical device, and thus the direction of advancement, to a desireddirection, without creating a magnetic force sufficient to advance themedical device.
 2. The method according to claim 1 wherein the magneticfield is applied with at least one electromagnet.
 3. The methodaccording to claim 1 wherein the magnetic field is applied with aplurality of electromagnets.
 4. The method according to claim 1 whereinthe direction of the applied magnetic field is different from thedesired direction of the medical device, and takes into account the lagin the responsiveness of the tip of the medical device to an appliedmagnetic field.
 5. A method of navigating a medical device through thebody, the method comprising the steps of: applying a magnet field from asource outside the body to a magnetically responsive element adjacentthe tip of the medical device, the field being of sufficient strengthand direction to change the direction of the tip of the medical device,without creating a magnetic force sufficient to advance the medicaldevice; mechanically pushing the medical device to advance the distalend of the medical device through the body in the direction in which thedistal tip has been magnetically oriented.
 6. The method according toclaim 5 wherein the magnetic field is applied with at least oneelectromagnet.
 7. The method according to claim 5 wherein the magneticfield is applied with a plurality of electromagnets.
 8. The methodaccording to claim 5 wherein the direction of the applied magnetic fieldis different from the desired direction of the medical device, and takesinto account the lag in the responsiveness of the tip of the medicaldevice to an applied magnetic field.